Abstract: We analyze the effects of radiative cooling on the pure baroclinic low-frequency waves under the approximation of equatorial β-plane and semi-geostrophic condition. The resul is show that rediative cooling doesn't provide the mere damping effects on the development of low-frequency waves. Under the delicate rediative-convective equilibrium, radiative effects will alter the phase speed and wave period, and bring about the broadband of phase velocity and wave period by adjusting the vertical profiles of diabatic heat lug. When the intensity of diabatic heat lug is moderate and appropriate, it is conductive to the development and sustaining of the low-frequency waves and their broadband phenomena, not the larger, the better. The radiative cool lug can not be neglectedin order to reach the moderate and appropriate intensity of diabatic heating.